# Dynamic Behaviour of Reinforced Concrete Structures: Analyses with a Strong Discontinuity Approach

[Doktorsavhandling]

Reinforced concrete is a widely used construction material. To obtain efficient design of new structures and to verify the real mechanical behaviour of existing ones, it is necessary to improve the understanding of advanced structural analyses of reinforced concrete structures. The presence of cracks is characteristic for concrete structures in service states as well as in ultimate limit states. In concrete micro-cracks are successively joined into macro-cracksduring loading, and the tensile strength of the material is obtained at this stage. As the propagation of micro-cracks is retarded in dynamic loading, the concrete shows a clear rate-dependent response. In this work a simplified experimental method is proposed for determination of the tensile strength of impact loaded concrete. However, the major part of the work concerns analyses of reinforced concrete.Degradation of concrete is today modelled by either a continuous or discontinuous approach. In this work the discontinuous one is applied to both quasi-static and dynamic loading conditions, and the classic fictitious crack model (FCM) is implemented in a general setting by using the extended finite element method (X-FEM). The mechanical response of the continuum is modelled with linear isotropic elastic material, while the intermediate fracture zones, of finite width, are lumped into (fictitious) cohesive cracks. The non-linear softening response of the cohesive cracks is modelled here with a new rate-dependent constitutive model based on anisotropic damage coupled to plasticity. In the X-FEM the continuous cracks are modelled as strong discontinuities of the displacement field, and their mechanical behaviour is introduced with traction-separation laws. The discontinuous displacement field in X-FEM is constructed in a new way by combining the standard continuous basis functions with supplementary discontinuous ones. The X-FEM format gives a superb kinematical performance. A crucial part of discontinuous modelling is the procedure for introduction of discontinuities. To determine whether or not failure occurs, a rate and pressure dependent fracture criterion of the Mohr-Coulomb type, with a smooth transition between failure in tension and shear, is used. The direction of the propagating discontinuity is determined by the classic Mohr-criterion. The application of discontinuous modelling to common types of reinforced concrete structures under both quasi-static and dynamic loading conditions is emphasized. Analyses of tensile wave propagation in reinforced concrete piles were carried out. Moreover, quasi-static and dynamic analyses were made for three-point bending tests of prestressed concrete railway sleepers and compared with experimental results.

**Nyckelord: **concrete, reinforcement, X-FEM, cohesive crack, anisotropic damage,

Denna post skapades 2006-08-25. Senast ändrad 2013-09-25.

CPL Pubid: 7427